Most civil law jurisdictions, including Poland, have a concept called "universal succession."
What this means is that the default rule is that the persons entitled to receive a decedent's property, as established by a notarized will or intestate succession in the absence of a will, collectively receive the property of the decedent subject to the debts of a decedent, with a legal obligation to share the proceeds and obligations between each other as provided by law and the terms of the Will.
But, it is possible, instead, to have the estate of a decedent formally administered. In these cases, the assets and liability of a decedent are formally determined and set off against each other. Successors of the decedent (either under a Will or intestate succession) are not subject to the debt's of the decedent if this is done, and instead, receive only the residuary assets of the estate remaining after the assets of the decedent have been used to pay the decedent's debts. This leaves only assets exempt from claims of creditors by statute (which are few) in the case of an insolvent estate, which is in most cases almost equivalent to giving up one's inheritance entirely.
In the exception case when an estate is formally administered in this fashion, this is normally done either by non-family executors, in cases where it seems sure that the estate will be insolvent, or by an executor chosen by the successors of the decedent or the Will, in cases where a complicated estate of a decedent is probably solvent, but its solvency is uncertain because it is hard to exactly value some assets and some liabilities, or because there is a likelihood that some unknown assets and/or some unknown liabilities exist.
Formal administration of a decedent's estate normally involves a process involving court filings or filings with a notary public that must be followed to affirmative elect to have a decedents estate formally administered. If this process is not followed within the specified time frame, the estate is usually, instead, governed by default process of universal succession.
The nitty gritty details of the process are beyond my knowledge, but that is the basic conceptual outline and baseline of how the process of handling decedent's estate is usually managed in civil law countries from which any country specific laws may deviate or further elaborate.
There is a summary of the law in Poland here. Basically, it provides that an heir's liability can be limited either by refusing the inheritance altogether or accepting it with the liability amounting to the value of the estate (so called "benefit of inventory"). So, in Poland, to get the benefits of formal administration the heirs need to prepare and file an inventory of the estate within six months of the date of death. They also have six months from the date of death to instead disclaim their inheritance and the obligations that come with it.
Under Polish law, the heirs should make declaration on accepting an
inheritance or refusing an inheritance within 6 months from the date
they became aware of the fact that they are to inherit after the
decedent. Where there is no declaration on acceptance or rejection of
inheritance within a period of 6 months, this will be considered as
the beneficiary accepting the inheritance with the benefit of
inventory. That is a good solution as the liability would be limited
to the value of the assets of the estate. Therefore, the heir would
not have to pay more debts then the inherited value. However, that
entails a duty to prepare an inventory list of the estate by the
heirs. That is why the refusal of inheritance is also worth
considering. . . .
Sometimes it is . . . better to take action and refuse the inheritance
instead of passively accepting the inheritance with the benefit of
inventory and dealing with unpaid debts which were not yours, even if
they do not exceed the estate's value.
The extent to which a debt arising by universal succession would be honored as a foreign judgment after established in the country where the decedent is domiciled at death is a question that honestly doesn't come up very much.
I don't know what preconditions a U.K. court would place on converting that debt to a U.K. money judgment.
I suspect that a U.S. court would be quite skeptical of recognizing a foreign judgment arising by universal succession because it would probably not meet the usual requirements of U.S. law for recognition of judgments, such as service of process on the resident judgment debtor, the existing of personal jurisdiction in personam over the resident judgment debtor in the court where the judgment was entered, and the lack of an adequate opportunity to litigate the obligation on the merits that was known to the resident judgment debtor.
But, I also wouldn't count on these defenses if I were a U.S. person and would instead seek to hire counsel in Poland to insist that the decedent's estate by having an inventory of the estate prepared and filed in a timely fashion, or by disclaiming the inheritance, based upon an evaluation of the benefits, risks, and administrative costs involved, and thus limiting the U.S. person's liability, unless the decedent's estate was solvent beyond any reasonable doubt.
In the U.S., in contrast, heirs or successors of a decedent are never subject to the debts of a decedent except to the extent the obligation arises from their own mismanagement of the administration of the estate, and typically only receive inheritances once all liabilities of the decedent have been adjudicated and paid out of the decedent's assets, making a U.S. probate proceeding, unlike a civil law universal successor proceeding, an in rem proceeding that only adjudicates rights to a specific collection of property and does not create new personal obligations for heirs that can be enforced with money judgments against those heirs.